Implementing a data definition facility driven by graph grammars

The implementation of a data definition facility based on graph transformations is discussed. The theory of graph grammars allows a precise characterization of these transformations, facilitating proofs of correctness.The implementation consists of an extension to PL/I, and utilizes the standard PL/I preprocessor.     

Correct transformation: From object-based graph grammars to PROMELA

Model transformation is an approach that, among other advantages, enables the reuse of existing analysis and implementation techniques, languages and tools. The area of formal verification makes wide use of model transformation because the cost of constructing efficient model checkers is extremely high. There are various examples of translations from specification and programming languages to the input languages of prominent model checking tools, like SPIN. However, this approach provides a safe analysis method only if there is a guarantee that the transformation process preserves the semantics of the original specification/program, that is, that the transformation is correct. Depending on the source and/or target languages, this notion of correctness is not easy to achieve. In this paper, we tackle this problem in the context of Object-Based Graph Grammars (OBGG). OBGG is a formal language suitable for the specification of distributed systems, with a variety of tools and techniques centered around the transformation of OBGG models. We describe in details the model transformation from OBGG models to PROMELA, the input language of the SPIN model checker. Amongst the contributions of this paper are: (a) the correctness proof of the transformation from OBGG models to PROMELA; (b) a generalization of this process in steps that may be used as a guide to prove the correctness of transformations from different specification/programming languages to PROMELA.     

Attribute grammars for scalable query processing on XML streams

We introduce the notion of XML Stream Attribute Grammars (XSAGs). XSAGs are the first scalable query language for XML streams (running strictly in linear time with bounded memory consumption independent of the size of the stream) that allows for actual data transformations rather than just document filtering. XSAGs are also relatively easy to use for humans. Moreover, the XSAG formalism provides a strong intuition for which queries can or cannot be processed scalably on streams. We introduce XSAGs together with the necessary language-theoretic machinery, study their theoretical properties such as expressiveness and complexity, and discuss their implementation.     

Propagation of constraints along model transformations using triple graph grammars and borrowed context

Fundamental properties of model transformations based on triple graph grammars (TGGs) have been studied extensively including syntactical correctness, completeness, termination and functional behavior. But up to now, it is an open problem how domain specific properties that are valid for a source model can be preserved along model transformations such that the transformed properties are valid for the derived target model. This question shows up in enterprise modeling. Here, modeling activities related to different domains are handled by different parties, and their models need to be consistent and integrated into one holistic enterprise model later on. So, support for decentralized modeling processes is needed. One technical aspect of the needed support in this case is the (bidirectional) propagation of constraints because that enables one party to understand and check the constraints of another party. Therefore, we analyze in the framework of TGGs how to propagate constraints from a source model to an integrated model and, afterwards, to a target model, such that, whenever the source model satisfies the source constraint, also the integrated and target model satisfy the corresponding integrated and target constraint. In our main new results we show under which conditions this is possible.     

Feature grammars for semantic analysis

In this paper, we present a formalism called feature grammar and its application to several problems of semantic analysis. Our extension concerns the structure of the feature value sets, which can be complex, and the definition of unification, which is dependent on this structure. Moreover, we introduce generation rules for feature symbols in order to determine well-formed symbols, which form the alphabet of a formal language for natural language analysis.     

One-sided forbidding grammars and selective substitution grammars

In one-sided forbidding grammars, the set of rules is divided into the set of left forbidding rules and the set of right forbidding rules. A left forbidding rule can rewrite a non-terminal if each of its forbidding symbols is absent to the left of the rewritten symbol in the current sentential form, while a right forbidding rule is applied analogically except that this absence is verified to the right. Apart from this, they work like ordinary forbidding grammars. As its main result, this paper proves that one-sided forbidding grammars are equivalent to selective substitution grammars. This equivalence is established in terms of grammars with and without erasing rules. Furthermore, this paper proves that one-sided forbidding grammars in which the set of left forbidding rules coincides with the set of right forbidding rules characterize the family of context-free languages. In the conclusion, the significance of the achieved results is discussed.     

A CKY parser for picture grammars

We study the complexity of the membership or parsing problem for pictures generated by a family of picture grammars: Siromoney's Context-Free Kolam Array grammars (coincident with Matz's context-free picture grammars). We describe a new parsing algorithm, which extends the Cocke, Kasami and Younger's classical parsing technique for string languages and preserves the polynomial time complexity.     

Extending OCL for OLAP querying on conceptual multidimensional models of data warehouses

The development of data warehouses begins with the definition of multidimensional models at the conceptual level in order to structure data, which will facilitate decision makers with an easier data analysis. Current proposals for conceptual multidimensional modelling focus on the design of static data warehouse structures, but few approaches model the queries which the data warehouse should support by means of OLAP (on-line analytical processing) tools. OLAP queries are, therefore, only defined once the rest of the data warehouse has been implemented, which prevents designers from verifying from the very beginning of the development whether the decision maker will be able to obtain the required information from the data warehouse. This article presents a solution to this drawback consisting of an extension to the object constraint language (OCL), which has been developed to include a set of predefined OLAP operators. These operators can be used to define platform-independent OLAP queries as a part of the specification of the data warehouse conceptual multidimensional model. Furthermore, OLAP tools require the implementation of queries to assure performance optimisations based on pre-aggregation. It is interesting to note that the OLAP queries defined by our approach can be automatically implemented in the rest of the data warehouse, in a coherent and integrated manner. This implementation is supported by a code-generation architecture aligned with model-driven technologies, in particular the MDA (model-driven architecture) proposal. Finally, our proposal has been validated by means of a set of sample data sets from a well-known case study.     

A unified framework for heterogeneous patterns

Knowledge patterns, such as association rules, clusters or decision trees, can be defined as concise and relevant information that can be extracted, stored, analyzed, and manipulated by knowledge workers in order to drive and specialize business decision processes. In this paper we deal with data mining patterns. The ability to manipulate different types of patterns under a unified environment is becoming a fundamental issue for any ‘intelligent’ and data-intensive application. However, approaches proposed so far for pattern management usually deal with specific and predefined types of patterns and mainly concern pattern extraction and exchange issues. Issues concerning the integrated, advanced management of heterogeneous patterns are in general not (or marginally) taken into account.     

Graph grammars with string-regulated rewriting

Multicellular organisms undergo a complex developmental process, orchestrated by the genetic information in their cells, in order to form a newborn individual from a fertilized egg. This complex process, not completely understood yet, is believed to have a key role in generating the impressive biotic diversity of organisms found on earth. Inspired by mechanisms of Eukaryotic genetic expression, we propose and analyse graph grammars with string-regulated rewriting. In these grammatical systems a genome sequence is represented by a regulatory string, a graph corresponds to an organism, and a set of graph grammar rules represents different forms of implementing cell division. Accordingly, a graph derivation by the graph grammar resembles the developmental process of an organism. We give examples of the concept and compare its generative power to the power of the traditional context-free graph grammars. We demonstrate that the power of expression increases when genetic regulation is included in the model, as compared to non-regulated grammars. Additionally, we propose a hierarchy of string-regulated graph grammars, arranged by expressive power. These results highlight the key role that the transmission of regulatory information during development has in the emergence of biological diversity.     

A linear time algorithm for monadic querying of indefinite data over linearly ordered domains

This paper demonstrates the generation of a linear-time query-answering algorithm based on the constructive proof of Higman’s lemma by Murthy and Russell [Proceedings of the 5th IEEE Symposium on Logic in Computer Science, 1990, p. 257–267]. The target problem is linear-time evaluation of a fixed disjunctive monadic query on an indefinite database over linearly ordered domains, first posed by van der Meyden [Proceedings of the 11th ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems, 1992, p. 331–345]. Van der Meyden showed the existence of a linear-time algorithm, but an explicit construction has, until now, not been reported.     

A probabilistic plan recognition algorithm based on plan tree grammars

We present the PHATT algorithm for plan recognition. Unlike previous approaches to plan recognition, PHATT is based on a model of plan execution. We show that this clarifies several difficult issues in plan recognition including the execution of multiple interleaved root goals, partially ordered plans, and failing to observe actions. We present the PHATT algorithm's theoretical basis, and an implementation based on tree structures. We also investigate the algorithm's complexity, both analytically and empirically. Finally, we present PHATT's integrated constraint reasoning for parametrized actions and temporal constraints.     

Inference for transition network grammars

This paper gives a brief introduction to transition networks and proposes an approach to the inference of transition network grammars.     

Function simulation,graph grammars and colourings

We prove that to any partial function ? defined on a finite set, there corresponds an infinite class of graphs that could be generated by a graph grammar such that each graph in the class represents the function in the sense that evaluation of the function at any point x of its domain can be simulated by finding the unique extension of a partial vertex colouring of the graph specified by x. We show that in the proposed setup, generating such simulator graphs as well as finding the colouring extensions can be computed effectively in polynomial time. We also discuss some applications of this scenario in producing instances of the graph colouring problem near its phase transition that can be applied in a cryptographic setting.     

A tabu search based approach for graph layout

This paper describes an automated tabu search based method for drawing general graph layouts with straight lines. To our knowledge, this is the first time tabu methods have been applied to graph drawing. We formulated the task as a multi-criteria optimization problem with a number of metrics which are used in a weighted fitness function to measure the aesthetic quality of the graph layout. The main goal of this work is to speed up the graph layout process without sacrificing layout quality. To achieve this, we use a tabu search based method that goes through a predefined number of iterations to minimize the value of the fitness function. Tabu search always chooses the best solution in the neighbourhood. This may lead to cycling, so a tabu list is used to store moves that are not permitted, meaning that the algorithm does not choose previous solutions for a set period of time. We evaluate the method according to the time spent to draw a graph and the quality of the drawn graphs. We give experimental results applied on random graphs and we provide statistical evidence that our method outperforms a fast search-based drawing method (hill climbing) in execution time while it produces comparably good graph layouts. We also demonstrate the method on real world graph datasets to show that we can reproduce similar results in a real world setting.     

Multi grammars

The theory of selective substitution grammars is an attempt to provide a common framework for a number of seemingly different rewriting systems. The core of a selective substitution grammar is its selector (language), which prescribes which occurrences of letters in a current sentential form must be rewritten. Three rudimentary forms of selectors, studied until now are sequential, parallel, and continuous selectors. This paper is concerned with building more involved selectors, starting with rudimentary ones and using operations of union and concatenation. The language generating power of several classes of rewriting systems obtained in this way is investigated.